Literal Genie: Like pretty much all of them, but not as extreme an example as many of them.
Miles Gloriosus: He is about mid-level in power as far as spirits go, but to hear him talk sometimes you'd think he's the top of the top. Though, djinni being very ancient, it's possible and even probable that he did participate in most of those historic events he brags about.
Smug Snake: Very much so, despite being semi-heroic. Most of his accomplishments are either exaggerated or through pure luck. Although he can pull off some genuinely amazing things when he gets down to brass tacks.
A notable example occurs near the climax of the first book: Bart describes himself as remaining calm and composed despite the dire situation. Immediately afterwards at the start of the next chapter, Nathaniel's third person perspective describes him as visibly panicking.
Evil Counterpart: To Bartimaeus. The author even describes the relationship between the two as the friendship gone horribly wrong and that many similarities they share only magnify the enmity between them.
Friendly Enemy: Possibly the most collected and well-mannered spirit, even while facing his worst enemies.
Jack of All Stats: He's significantly stronger than Bartimaeus, and much more versatile and intelligent than Jabor. While Bartimaeus generally succeed in outmaneuvering him, it's clear that he considers Faquarl the biggest threat on the table.
Smug Snake: A rare protagonist example. In the second book he tries to come off as unflappable and stylish, but he's pretty much as slimy as every other government magician. He gets better in the third book.
Teen Genius: He's a better magician than most grown men.
Used to Be a Sweet Kid: Until certain events embittered him to the world. Like Ms. Lutyens getting sacked and Mrs. Underwood's death.
Vitriolic Best Buds: Kind of with Bartimaeus. Despite their constant bickering, he does grow to respect and rely on him a lot.
One of the series' main protagonists. She is a commoner who later joins the the Resistance to fight the injustices of the magicians.
Paper Tiger: He pretends to be powerful and respected, but he's a mediocre fool who's quick to cringe and toady when up against more powerful magicians like Lovelace.
Wizard Classic: Strives to maintain the traditional "bushy beard and eyebrows" look. Bartimaeus notes that this is a good indication he's a second-rate poser trying to big himself up (and he's absolutely right.)
Big Bad Wannabe: An unusual example. In the first two books he's The Man Behind the Man to the two Big Bads, yet when he tries to step into the spotlight and enact his own plot in the third book, he's quickly manipulated and killed by Faquarl, who is pretending to be his Number Two Hopkins.
Chekhov's Gunman: He's mentioned in the first book by a few characters but only becomes prominent in the second where he becomes Nathaniel's ally. He's also seen briefly in disguise retreating from Lovelace's manor before the climax of the first book, having helped construct the massive summoning circle to contain Ramuthra.
Almighty Janitor: Is a very powerful magician, but he prefers to hold a first line job in his franchise.
Ambiguously Evil: Although he is shown as an acquitance to Lovelace and Schyler and the man who sold them the summoning horn, he actually doesn't belong to their conspirating circle, and appears to be completely unaware of it.
Badass Grandpa: He is the only high-level magician to survive the events in the third book, and the only of them who puts a fight when Makepeace's spirits capture all them. In fact, given his lack of spirit aides in contrast with the rest of magicians, he could be one of the few of them who can hold his own without help from demons.